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<p>In terms of a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_{8}\phi _{7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>8</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> transformation formula due to Watson, the Chinese remainder theorem for coprime polynomials, and the ‘creative microscoping’ method introduced by Guo and Zudilin, we give some new parametric <i>q</i>-supercongruences modulo the fourth power of a cyclotomic polynomial. Meanwhile, one of our main results is a parametric generalization of Long and Ramakrishna’s supercongruence.</p>

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Some parametric q-supercongruences modulo the fourth power of a cyclotomic polynomial

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • He-Xia Ni

摘要

In terms of a \(_{8}\phi _{7}\) 8 ϕ 7 transformation formula due to Watson, the Chinese remainder theorem for coprime polynomials, and the ‘creative microscoping’ method introduced by Guo and Zudilin, we give some new parametric q-supercongruences modulo the fourth power of a cyclotomic polynomial. Meanwhile, one of our main results is a parametric generalization of Long and Ramakrishna’s supercongruence.